Fundamentals of Accounting · Partnership and LLP Accounts

Admission of a Partner: Accounting Problems Explained

Updated 11 October 2026 · Fact-checked

Admission of a partner means a new person joins the firm, so the old partnership ends and a new one begins. To solve problems, find the new profit ratio and the sacrificing ratio, treat goodwill, revalue assets and liabilities, share reserves among old partners, then record the new partner's capital and adjust capitals if asked.

Understand Admission of a Partner

When a new partner joins, the old partnership is reconstituted. The new partner gets a share of future profits. That share has to come from somewhere, so the old partners give up part of their own share. This is the sacrifice.

The new partner also gets a right to the firm's reputation and to profits built up in the past. So the old partners must be paid for this. This is why we deal with goodwill, revaluation and reserves at the time of admission.

The key idea is fairness between old and new partners. Anything earned or lost before the admission belongs to the old partners. So the revaluation profit or loss, the reserves and the accumulated profits are shared in the old ratio. Anything from the date of admission belongs to all partners in the new ratio.

Goodwill is the value of the firm's name and customer base. The new partner pays for his share of it. This payment is called the premium for goodwill. It is usually paid in cash and shared by the old partners in their sacrificing ratio, because they are the ones giving up profit share. If the new partner does not bring goodwill in cash, you may have to find the hidden goodwill from the capitals.

Finally, partners may agree that capitals should match the profit sharing ratio. Then you work out the new capitals and settle the difference in cash or through current accounts.

Key rules to remember

Sacrificing ratio: Sacrificing share = Old share − New share (for each old partner); If the question does not say how the old partners give up shares, assume they sacrifice in their old ratio. Then the sacrificing ratio equals the old ratio.
New profit sharing ratio (equal sacrifice in old ratio): Old partner's new share = Old share × (1 − New partner's share); Example: old share 3/5, new partner gets 1/5. New share = 3/5 × 4/5 = 12/25.
Goodwill brought by the new partner: Premium = Firm's goodwill × New partner's share; The premium is shared by old partners in the sacrificing ratio, not the old ratio unless both are the same.
Hidden goodwill: Total capital of new firm = New partner's capital ÷ His share Goodwill of firm = Total capital of new firm − (Adjusted capitals of old partners + New partner's capital); Adjusted capitals include revaluation result and reserves. Use this only when goodwill is not given and the new partner's capital and share are known.
Revaluation account: Loss: Dr Revaluation A/c, Cr Asset A/c (decrease in value) or Cr Liability A/c (increase in value) Profit: Dr Asset A/c (increase in value) or Dr Liability A/c (decrease in value), Cr Revaluation A/c; Net profit or loss goes to old partners' capital accounts in the old ratio.
Reserves and accumulated profits: Credit old partners' capital accounts in the old ratio; Applies to general reserve, profit and loss balance and other reserves. A debit balance in P&L is shared as a loss.
Journal entry for premium in cash: Bank A/c Dr (capital + premium) To New partner's Capital A/c To Premium for Goodwill A/c Premium for Goodwill A/c Dr To Old partners' Capital A/cs (sacrificing ratio); If goodwill is raised in the books, it is credited to old partners in their sacrificing ratio. In the hidden goodwill example this equals the old ratio, because the sacrifice is in the old ratio.

How to solve Admission of a Partner questions

Use the same order every time. It keeps the entries clean and helps you pick up step marks even if one figure goes wrong.

1Write the old ratio and the new partner's share. Find the new ratio and the sacrificing ratio. If a sacrifice or gain is stated, use that. Otherwise take the new partner's share from old partners in their old ratio.
2Prepare the Revaluation Account. Debit losses and decreases in assets, or increases in liabilities. Credit gains. Share the net result in the old ratio.
3Distribute reserves and accumulated profits among old partners in the old ratio.
4Treat goodwill. If premium is brought in cash, credit it to old partners in the sacrificing ratio. If goodwill is hidden, calculate it first from the capitals.
5Record the new partner's capital and the cash brought in.
6Prepare the Partners' Capital Accounts with opening balances, reserves, revaluation result, goodwill and capital brought in.
7If capitals must be adjusted to the new ratio, calculate the new capitals and settle the difference in cash or current accounts.
8Check that total capitals equal the net assets in the new balance sheet.

Quickest way: Quick route through an admission problem

When to use it: Use this when time is short and the question gives only a few items, such as capital, premium and a reserve.

Compute the new ratio and sacrificing ratio first, in fractions with a common denominator.
Open a capital account table in columns for each old partner and the new partner. Put the opening balance on top.
Add rows for reserve, revaluation result and goodwill share. Fill each row in one go using the right ratio.
Total each column to get closing capitals. Do the bank entry on the side.
Check: sum of capitals = old total capital + reserves + revaluation result + cash brought in (+ any goodwill raised).

Common mistakes in Admission of a Partner

Sharing the revaluation profit or loss in the new ratio.
Students see the new partner on the balance sheet and include him in everything.
Fix: Revaluation relates to the period before admission, so it goes to old partners in the old ratio. The new partner gets none of it.
Crediting the premium for goodwill in the old ratio when the sacrifice is different.
Students assume the old and sacrificing ratios are always equal.
Fix: Always calculate the sacrificing ratio as old share minus new share. Use it for goodwill premium.
Reversing debit and credit in the Revaluation Account.
Students confuse the account's side with the asset's side.
Fix: A loss or fall in an asset is a debit to Revaluation. A gain is a credit. Remember: Revaluation A/c is like a mini profit and loss account.
Forgetting to distribute reserves and the profit and loss balance.
The balance sheet items are listed but not used in the entries.
Fix: Tick off every reserve and accumulated profit in the balance sheet. Credit each to old partners in the old ratio.
Using wrong total capital when finding hidden goodwill.
Students forget to adjust old capitals for reserves and revaluation, or leave out the new partner's capital.
Fix: First adjust old capitals, then add the new partner's capital. Compare that sum with the total capital implied by his share.
Treating the premium as part of the new partner's capital.
Both amounts are brought in cash and the bank entry is one figure.
Fix: Split the cash. The capital part goes to the new partner's capital account. The premium goes to old partners.

Worked examples

Example 1

A and B share profits in the ratio 3:2. Their capitals are ₹1,50,000 and ₹1,00,000. They have a general reserve of ₹25,000. C is admitted for 1/5 share and brings ₹1,00,000 as capital and ₹40,000 as premium for goodwill in cash. The building is appreciated by ₹20,000 and stock is reduced by ₹5,000. Find the new ratio and sacrificing ratio and prepare the partners' closing capitals.

Show the solution

C takes 1/5, so A and B share 4/5 in 3:2. New share of A = 3/5 × 4/5 = 12/25. New share of B = 2/5 × 4/5 = 8/25. C = 1/5 = 5/25. New ratio = 12:8:5.
Sacrifice: A = 3/5 − 12/25 = 15/25 − 12/25 = 3/25. B = 2/5 − 8/25 = 10/25 − 8/25 = 2/25. Sacrificing ratio = 3:2.
Revaluation: gain on building ₹20,000, loss on stock ₹5,000. Net profit = ₹15,000. A gets 3/5 = ₹9,000. B gets 2/5 = ₹6,000.
General reserve ₹25,000 in old ratio: A ₹15,000, B ₹10,000.
Premium ₹40,000 in sacrificing ratio 3:2: A ₹24,000, B ₹16,000.
Closing capital of A = 1,50,000 + 9,000 + 15,000 + 24,000 = ₹1,98,000.
Closing capital of B = 1,00,000 + 6,000 + 10,000 + 16,000 = ₹1,32,000.
Closing capital of C = ₹1,00,000. Cash brought in = ₹1,40,000.

Answer: New ratio 12:8:5. Sacrificing ratio 3:2. Closing capitals: A ₹1,98,000, B ₹1,32,000, C ₹1,00,000.

Example 2

X and Y share profits 2:1. Their capitals are ₹3,00,000 and ₹1,50,000. Z is admitted for 1/4 share and brings ₹2,00,000 as capital. He does not bring anything for goodwill. Assets and liabilities are correctly valued and there are no reserves. Find the goodwill of the firm and the closing capitals if goodwill is raised and credited to X and Y.

Show the solution

Z's capital ₹2,00,000 is for 1/4 share. Total capital of new firm = 2,00,000 ÷ 1/4 = ₹8,00,000.
Actual capitals of all partners = 3,00,000 + 1,50,000 + 2,00,000 = ₹6,50,000.
Hidden goodwill = 8,00,000 − 6,50,000 = ₹1,50,000.
Goodwill is credited to old partners in the old ratio 2:1 (as the sacrifice is in the old ratio here). X gets ₹1,00,000. Y gets ₹50,000.
Entry: Goodwill A/c Dr ₹1,50,000; To X's Capital ₹1,00,000; To Y's Capital ₹50,000.
Closing capital of X = 3,00,000 + 1,00,000 = ₹4,00,000.
Closing capital of Y = 1,50,000 + 50,000 = ₹2,00,000.
Closing capital of Z = ₹2,00,000. Total = ₹8,00,000, which matches the total capital of the new firm. Z's share = 2,00,000 ÷ 8,00,000 = 1/4, which is correct.

Answer: Goodwill of the firm = ₹1,50,000. Closing capitals: X ₹4,00,000, Y ₹2,00,000, Z ₹2,00,000.

Exam tips

Start every answer with the new ratio and sacrificing ratio. Show the fraction work, because marks are given for it.
Label every ratio you use in the answer, such as 'old ratio' or 'sacrificing ratio'. Examiners look for the right ratio on each item.
Read the question for the words 'goodwill not brought in cash', 'capitals to be adjusted' or 'goodwill to be written off'. Each changes the entries.
Draw the Revaluation Account and capital accounts in a neat format. Partial marks are given for correct parts even if the total is wrong.
Before you finish, check that total capitals match the net assets, or that the new partner's capital matches his share of total capital.

Practice questions from Partnership and LLP Accounts

Admission of a Partner in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Admission of a Partner: frequently asked questions

What is the sacrificing ratio and how do I calculate it?

The sacrificing ratio is the ratio in which old partners give up their share to the new partner. Calculate it as old share minus new share for each old partner. If nothing is stated, the old partners sacrifice in their old ratio.

Who gets the premium for goodwill on admission?

Old partners get it, in their sacrificing ratio. They are the ones who give up profit share to the new partner. If the firm keeps the premium in cash, the old partners' capital accounts are credited.

Why is the revaluation profit shared in the old ratio?

The change in value of assets and liabilities happened before the new partner joined. So the gain or loss belongs to the old partners. They share it in the ratio they used to share profits.

What is hidden goodwill?

Hidden goodwill is goodwill that is not given directly but can be found from the new partner's capital and share. Find the total capital of the new firm from his capital and share. Then subtract the actual total capital, after adjustments. The difference is the goodwill of the firm.

Do I need to adjust capitals in every admission problem?

No. Do it only when the question says capitals should be in the new profit sharing ratio. Otherwise, closing capitals after the entries are simply carried forward.